Is the United States in the middle of a healthcare bubble?

Abstract

Objectives

This study investigates the possibility of multiple healthcare bubbles in the US healthcare market.

Methods

We first applied the newly developed Generalized Sup ADF test to locate multiple healthcare bubble episodes and then estimated the switching regression model specifying multiple healthcare bubble periods to evaluate to what extent macroeconomic variables (such as the interest rate, public debt, and fiscal deficit) and public financing healthcare programs influence the magnitude of healthcare bubbles in terms of the deviation of the medical care price inflation from either the overall price inflation or the money wage growth.

Results

Our results show that expansionary monetary and fiscal policies play important roles in determining the deviation of the medical care price inflation from the overall price inflation and that the net government debt has a positive impact on the deviation of the medical care price inflation from the money wage growth. The US healthcare market is now in the middle of a healthcare bubble, and this healthcare bubble has developed slowly and has lasted for approximately 3 decades, mirroring an increased societal preference for healthcare.

Conclusions

Policymakers in the US should cautiously consider the fact that healthcare bubbles must imply a misallocation of resources into healthcare, leading to negative consequences on the sustainability of the healthcare system.

Appendix

The technical presentation of the empirical procedure to identify the multiple episodes of healthcare bubbles is described as follows: As for the conventional left-tailed unit root test, the empirical model for the GSADF test can be specified as Eq. (2) below:

$$\Delta p_{\text{t}} = \alpha_{{r_{1} ,r_{2} }} + \delta_{{r_{1} ,r_{2} }} p_{{{\text{t}} - 1}} + \sum\limits_{j = 1}^{k} {\varphi_{{r_{1} ,r_{2} }}^{j} \Delta p_{{{\text{t}} - {\text{j}}}} + \varepsilon_{\text{t}} }$$

(2)

Equation (2) is the standard Augmented Dickey-Fuller (ADF) regression model, where p _t is the observed relative medical care price index (RPI), medical care price-to-wage ratio (MTWR), or overall price-to-wage ratio (PTWR) at time t. Δp _t−j represents the jth difference of p _t–j . k is the lag order. ɛ _t denotes the error term. r ₁ and r ₂ represent fractions of the total sample size N, which defines the starting point and ending point of the sample (or subsample period) N. The number of observations in Eq. (2) is $N_{w} = [N_{{r_{w} }} ]$, where [•] represents the integer part of its argument and r _w  = r ₂–r ₁ is the fractional window size. The ADF statistic estimated from Eq. (2) is denoted by $ADF_{{r_{1} }}^{{r_{2} }}$. In order to obtain the GSADF statistic, Phillips et al. [3] proposed a repeatedly backward rolling window method to construct the backward SADF statistic as Eq. (3) below:

$$BSADF_{{r_{2} }} (r_{0} ) = \mathop {\sup }\limits_{{r_{1} \in [r_{0} ,r_{2} - r_{0} ]}} \{ ADF_{{r_{1} }}^{{r_{2} }} \}$$

(3)

where, $BSADF_{{r_{2} }} (r_{0} )$ is the backward SADF statistic for each r ₁ ∊ [r ₀, r ₂–r ₀] (r ₀ is the initial fractional starting point), and the GSADF statistic [specified in Eq. (4) below] is the sup value of the backward SADF statistic sequence for each r ₂ ∊ [r ₀, 1].

$$GSADF(r_{0} ) = \mathop {\sup }\limits_{{r_{2} \in [r_{0} ,1]}} \{ BSADF_{{r_{2} }} (r_{0} )\}$$

(4)

The asymptotic distribution of the GSADF statistic [expressed as Eq. (5) below] can be derived from the null hypothesis that p _t is a random walk with an asymptotically negligible drift [3].

$$GSADF(r_{0} )\mathop \to \limits^{d} \mathop {\sup }\limits_{{r_{2} \in [r_{0} ,1],r_{1} \in [0,r_{2} - r_{0} ]}} \left\{ {\frac{{\frac{1}{2}r_{w} \left[ {W(r_{2} )^{2} - W(r_{1} )^{2} - r_{w} } \right] - \int_{{r_{1} }}^{{r_{2} }} {W(r){\text{d}}r[W(r_{2} ) - W(r_{1} )]} }}{{r_{w}^{1/2} \left\{ {r_{w} \int_{{r_{1} }}^{{r_{2} }} {W(r)^{2} {\text{d}}r - \left[ {\int_{{r_{1} }}^{{r_{2} }} {W(r){\text{d}}r} } \right]^{2} } } \right\}^{1/2} }}} \right\}$$

(5)

where W is the standard Wiener process. Since the asymptotic distribution of the GSADF statistic is a non-standard distribution, we apply the Monte Carlo simulation method (with 5,000 replications) to calculate the 100 (1−α) % critical value of the GSADF statistic.